The correct graph between the frequency $n$ and square root of density ($\rho$) of a wire, keeping its…

The correct graph between the frequency $n$ and square root of density ($\rho$) of a wire, keeping its length, radius and tension constant, is Four graphs plotting frequency n against sqrt(rho). (a) shows a convex decreasing curve; (b) shows a horizontal line; (c) shows a concave decreasing curve; (d) shows a curve increasing from zero.
  1. Graph (a)
  2. Graph (b)
  3. Graph (c)
  4. Graph (d)

Solution

As, frequency, $n = \frac{p}{2l} \sqrt{\frac{T}{\pi r^2 \rho}} \Rightarrow n \propto \frac{1}{\sqrt{\rho}}$ i.e. Graph between $n$ and $\sqrt{\rho}$ will be hyperbola.

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